In recent years, there have been proposed and developed various belt-drive continuously variable transmissions (CVTs), which enable an actual transmission ratio to be steplessly adjusted or feedback-controlled toward a desired transmission ratio. As is generally known, a belt-drive continuously variable transmission uses a drive belt (usually, a single segmented steel belt) running in a pair of variable-width pulleys, that is, primary and secondary pulleys whose V grooves are aligned with each other, to provide varying gear ratios or pulley ratios or transmission ratios. In more detail, the V groove of the primary pulley, to which input rotation is transmitted from an engine, is constructed by a stationary flange and an adjustable flange axially slidable for varying the width of the V groove of the primary pulley by way of a “primary pulley pressure”. The V groove of the secondary pulley, which is connected via a gear train to drive wheels, is constructed by a stationary flange and an adjustable flange for varying the width of the V groove of the secondary pulley by way of a “secondary pulley pressure”. Each of the primary and secondary pulley pressures is produced by properly modulating a line pressure, which is used as an initial pressure. Actually, the adjustable flange of the primary pulley is forced toward the associated stationary flange by the primary pulley pressure, and simultaneously the adjustable flange of the secondary pulley is forced toward the associated stationary flange by the secondary pulley pressure. This enables power transmission between the primary and secondary pulleys via the drive belt (the segmented steel belt), while keeping the drive belt in friction-contact with the V grooves of the primary and secondary pulleys. One such belt-drive continuously variable transmission has been disclosed in Japanese Patent Provisional Publication No. 11-37237 (hereinafter is referred to as “JP11-37237”). During speed-change operation, a ratio-change control actuator, such as a step motor, is moved or actuated toward an operative position corresponding to the number of angular steps based on a desired transmission ratio (a desired pulley ratio), to change the primary pulley pressure. As a result, the differential pressure between the primary and secondary pulley pressures, corresponding to the desired transmission ratio, is produced to change the widths of the V grooves of the primary and secondary pulleys and thus to achieve the desired transmission ratio. As can be appreciated from the above, a downshift is achieved by increasing the width of the V groove of the primary pulley by way of a reduction in the primary pulley pressure and by decreasing the width of the V groove of the secondary pulley by way of a rise in the secondary pulley pressure. In case that a downshifting action, which is achieved by a drop in the primary pulley pressure, is comparatively quick, in particular, in case that a rapid downshift is executed under a condition that input rotation transferred into the CVT is relatively low, for example, just before the vehicle is stopped, there is an increased tendency for a temporary lack of the actual primary pulley pressure to occur. In such a case, undesired slippage (frictional losses or power losses) between the drive belt and the variable-width pulley tends to occur, thereby reducing the durability of the drive belt owing to drive-belt wear. This leads to the problem of a remarkably reduced durability of the CVT. One way to avoid this is to constantly set each of primary and secondary pulley pressures to a relatively high-pressure level through all speed-change operations containing a downshifting period. However, in order to keep the line pressure constantly at a high-pressure level, an increased margin (or a proper offset or a proper steady-state deviation) has to be given with respect to the line pressure, serving as an initial pressure of each of the primary and secondary pulley pressures. This means a wasteful increase in the load on an engine-driven oil pump that produces the line pressure, thus deteriorating fuel economy and increasing fuel consumption. For the reasons discussed above, it is desirable to keep the speed-change hydraulic pressure (in particular, the primary pulley pressure) to just below a critical pressure level where undesirable slippage between the variable-width pulley and the drive belt would start to develop. However, it is difficult to hold the speed-change hydraulic pressure to just below the critical pressure level for slippage prevention, because of various factors, that is, differences in quality of hydraulic parts used in a hydraulic modulator of the CVT, drive-belt wear, input-torque fluctuations, disturbance torque, a delay in response of the speed-change hydraulic pressure to a rapid change in input torque, and the like. Thus, it would be desirable to provide a means by which a state that undesirable slippage between a variable-width pulley and a drive belt may start to develop can be foretold or predicted or precognized, so as to prevent or suppress an undesirable drop in the primary pulley pressure from developing.